Major recent advances in the theoretical study of heterogeneous nucleation on macroscopic wettable centers of different nature are reviewed in the context of the classical scheme which uses the nucleation thermodynamics of a new phase to calculate the key nucleation kinetics characteristics. The review centers on heterogeneous nucleation kinetics under conditions where a metastable state of the initial phase gradually forms-a situation in which the factors bringing about this process and forcing the phase further into the metastability region also remain active after the intense phase transition has began. The formulation and control of the consistency conditions for all the thermodynamic and kinetic elements of the theory are emphasized. The interface thermodynamics is discussed in detail and a careful kinetics analysis is performed for the stage at which the main number of stably growing nuclei of the new phase is formed around wettable nuclei consisting of soluble, insoluble, surface active, or surface inactive material. The features Common to barrier and barrierless heterogeneous nucleation processes are discussed, which open new possibilities in the experimental study of the phenomenon and offer new practical applications of the theory.